# Confidence intervals for beta regression

I have used the betareg package in R to fit a regression. My question is: how do I calculate confidence intervals for betaregression in R?

• Questions solely about how software works are off-topic here, but you may have a real statistical question buried here. You may want to edit your question to clarify the underlying statistical issue. You may find that when you understand the statistical concepts involved, the software-specific elements are self-evident or at least easy to get from the documentation. Sep 9, 2016 at 23:03
• What do you mean by "confidence interval" in this context? Do you want a CI for some parameter? Do you want a conficence band for the model? Do you want prediction intervals for some y-hat values? Etc. Sep 9, 2016 at 23:05

The beta likelihood is not a regular exponential family, so constructing interval estimates for such two parameter families is not easily done. I think Zeileis was wise not to implement any de-facto methods for confint. The cited article Ospina suggests that bootstrap interval estimates perform best. The package boot has some methods, but bootstrapping is also easily done "by-hand" in R.
• One more comment about confint: This is not for confidence intervals of fitted values but for confidence intervals of coefficient estimates. The default method works if there is a coef and a vcov methods (which is the case for betareg) and returns Wald confidence intervals based on the asymptotic normal distribution of the maximum likelihood parameter estimates. Sep 10, 2016 at 6:47
• @AchimZeileis A celebrity sighting on my post! Indeed I assumed the OP was asking about CIs for the parameter estimates. Help me understand something: Wald based CIs using coef and vcov methods are not necessarily asymptotically correct for MLEs unless the likelihood is a regular exponential family. Take linear mixed models from the lme4 package, they don't recommend creating inference from the information matrix and coefficients from the fixed effects. They use profile/bootstrap CI methods, is this to improve efficiency or reduce bias? Sep 10, 2016 at 14:33
• (Not sure about the celebrity thing...anyways:) Of course, the maximum likelihood estimates and their associated confidence intervals are biased in finite samples. As Kosmidis & Firth (2010, EJS) showed, the bias in beta regressions can become quite large, especially for the precision estimates. They have suggested a generic approach for reducing the bias and we have implemented this in betareg(..., method = "BR"). Sep 10, 2016 at 15:26